Simplificación general
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___
-\/ 2 *(2 + x)
------------------------------
_________ / 2\
2*\/ 1 + 2*x *\1 + 4*x + 4*x /
$$- \frac{\sqrt{2} \left(x + 2\right)}{2 \sqrt{2 x + 1} \left(4 x^{2} + 4 x + 1\right)}$$
-sqrt(2)*(2 + x)/(2*sqrt(1 + 2*x)*(1 + 4*x + 4*x^2))
0.353553390593274*(0.5 + x)^(-1.5)*(-2.82842712474619 + 0.176776695296637*(5.0 + 5.0*x - 10.0*x^2)/(0.5 + x)^2 + 1.4142135623731*(-3.0 + 12.0*x)/(2.0 + 4.0*x))
0.353553390593274*(0.5 + x)^(-1.5)*(-2.82842712474619 + 0.176776695296637*(5.0 + 5.0*x - 10.0*x^2)/(0.5 + x)^2 + 1.4142135623731*(-3.0 + 12.0*x)/(2.0 + 4.0*x))
Compilar la expresión
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/ 2 \
___ | -3 + 12*x 5 - 10*x + 5*x|
\/ 2 *|-2 + --------- + ---------------|
| 2 + 4*x 2 |
\ 2*(1 + 2*x) /
----------------------------------------
3/2
(1 + 2*x)
$$\frac{\sqrt{2} \left(-2 + \frac{12 x - 3}{4 x + 2} + \frac{- 10 x^{2} + 5 x + 5}{2 \left(2 x + 1\right)^{2}}\right)}{\left(2 x + 1\right)^{\frac{3}{2}}}$$
sqrt(2)*(-2 + (-3 + 12*x)/(2 + 4*x) + (5 - 10*x^2 + 5*x)/(2*(1 + 2*x)^2))/(1 + 2*x)^(3/2)
Abrimos la expresión
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/ / 2\\
___ | 3*(-1 + 4*x) 5*\1 + x - 2*x /|
\/ 2 *|-2 + ------------ + ----------------|
| 2*(1 + 2*x) 2 |
\ 2*(1 + 2*x) /
--------------------------------------------
3/2
(1 + 2*x)
$$\frac{\sqrt{2} \left(-2 + \frac{3 \left(4 x - 1\right)}{2 \left(2 x + 1\right)} + \frac{5 \left(- 2 x^{2} + \left(x + 1\right)\right)}{2 \left(2 x + 1\right)^{2}}\right)}{\left(2 x + 1\right)^{\frac{3}{2}}}$$
sqrt(2)*(-2 + 3*(-1 + 4*x)/(2*(1 + 2*x)) + 5*(1 + x - 2*x^2)/(2*(1 + 2*x)^2))/(1 + 2*x)^(3/2)
Denominador racional
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___ 5/2 ___ _________ ___ 3 _________ ___ 5/2 ___ _________
- 14*\/ 2 *(1 + 2*x) + 10*\/ 2 *\/ 1 + 2*x - 40*\/ 2 *x *\/ 1 + 2*x + 8*x*\/ 2 *(1 + 2*x) + 30*x*\/ 2 *\/ 1 + 2*x
--------------------------------------------------------------------------------------------------------------------------
/ 4 2 3\
2*(2 + 4*x)*\1 + 8*x + 16*x + 24*x + 32*x /
$$\frac{- 40 \sqrt{2} x^{3} \sqrt{2 x + 1} + 8 \sqrt{2} x \left(2 x + 1\right)^{\frac{5}{2}} + 30 \sqrt{2} x \sqrt{2 x + 1} - 14 \sqrt{2} \left(2 x + 1\right)^{\frac{5}{2}} + 10 \sqrt{2} \sqrt{2 x + 1}}{2 \left(4 x + 2\right) \left(16 x^{4} + 32 x^{3} + 24 x^{2} + 8 x + 1\right)}$$
(-14*sqrt(2)*(1 + 2*x)^(5/2) + 10*sqrt(2)*sqrt(1 + 2*x) - 40*sqrt(2)*x^3*sqrt(1 + 2*x) + 8*x*sqrt(2)*(1 + 2*x)^(5/2) + 30*x*sqrt(2)*sqrt(1 + 2*x))/(2*(2 + 4*x)*(1 + 8*x + 16*x^4 + 24*x^2 + 32*x^3))
Unión de expresiones racionales
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___ / 2 \
\/ 2 *\5 - 10*x + 5*x + (1 + 2*x)*(-7 + 4*x)/
----------------------------------------------
7/2
2*(1 + 2*x)
$$\frac{\sqrt{2} \left(- 10 x^{2} + 5 x + \left(2 x + 1\right) \left(4 x - 7\right) + 5\right)}{2 \left(2 x + 1\right)^{\frac{7}{2}}}$$
sqrt(2)*(5 - 10*x^2 + 5*x + (1 + 2*x)*(-7 + 4*x))/(2*(1 + 2*x)^(7/2))
___
-\/ 2 *(2 + x)
---------------
5/2
2*(1 + 2*x)
$$- \frac{\sqrt{2} \left(x + 2\right)}{2 \left(2 x + 1\right)^{\frac{5}{2}}}$$
-sqrt(2)*(2 + x)/(2*(1 + 2*x)^(5/2))
/ 2 \
___ | -3 + 12*x 5 - 10*x + 5*x|
\/ 2 *|-2 + --------- + ---------------|
| 2 + 4*x 2 |
\ 2*(1 + 2*x) /
----------------------------------------
3/2
(1 + 2*x)
$$\frac{\sqrt{2} \left(-2 + \frac{12 x - 3}{4 x + 2} + \frac{- 10 x^{2} + 5 x + 5}{2 \left(2 x + 1\right)^{2}}\right)}{\left(2 x + 1\right)^{\frac{3}{2}}}$$
/ 5 2 5*x \
| - - 5*x + --- |
___ | 2 2 -3 + 12*x|
\/ 2 *|-2 + -------------- + ---------|
| 2 2 + 4*x |
\ (1 + 2*x) /
---------------------------------------
3/2
(1 + 2*x)
$$\frac{\sqrt{2} \left(-2 + \frac{12 x - 3}{4 x + 2} + \frac{- 5 x^{2} + \frac{5 x}{2} + \frac{5}{2}}{\left(2 x + 1\right)^{2}}\right)}{\left(2 x + 1\right)^{\frac{3}{2}}}$$
sqrt(2)*(-2 + (5/2 - 5*x^2 + 5*x/2)/(1 + 2*x)^2 + (-3 + 12*x)/(2 + 4*x))/(1 + 2*x)^(3/2)
/ ___ ___\
-\2*\/ 2 + x*\/ 2 /
--------------------------------------------------
_________ _________ 2 _________
2*\/ 1 + 2*x + 8*x*\/ 1 + 2*x + 8*x *\/ 1 + 2*x
$$- \frac{\sqrt{2} x + 2 \sqrt{2}}{8 x^{2} \sqrt{2 x + 1} + 8 x \sqrt{2 x + 1} + 2 \sqrt{2 x + 1}}$$
-(2*sqrt(2) + x*sqrt(2))/(2*sqrt(1 + 2*x) + 8*x*sqrt(1 + 2*x) + 8*x^2*sqrt(1 + 2*x))
Parte trigonométrica
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/ 2 \
___ | -3 + 12*x 5 - 10*x + 5*x|
\/ 2 *|-2 + --------- + ---------------|
| 2 + 4*x 2 |
\ 2*(1 + 2*x) /
----------------------------------------
3/2
(1 + 2*x)
$$\frac{\sqrt{2} \left(-2 + \frac{12 x - 3}{4 x + 2} + \frac{- 10 x^{2} + 5 x + 5}{2 \left(2 x + 1\right)^{2}}\right)}{\left(2 x + 1\right)^{\frac{3}{2}}}$$
sqrt(2)*(-2 + (-3 + 12*x)/(2 + 4*x) + (5 - 10*x^2 + 5*x)/(2*(1 + 2*x)^2))/(1 + 2*x)^(3/2)